Integral of -x+4 dx

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$$\int\limits_{0}^{1} \left(4 - x\right)\, dx$$

Integral(-x + 4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- \frac{x^{2}}{2}$
The result is: $- \frac{x^{2}}{2} + 4 x$
Now simplify:

$\frac{x \left(8 - x\right)}{2}$
Add the constant of integration:

$\frac{x \left(8 - x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(8 - x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         2
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 | (-x + 4) dx = C + 4*x - --
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$$\int \left(4 - x\right)\, dx = C - \frac{x^{2}}{2} + 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/2

$$\frac{7}{2}$$

7/2

$$\frac{7}{2}$$

7/2

Numerical answer [src]

3.5

3.5

The graph

Use the examples entering the upper and lower limits of integration.